Self-phase modulation in long-geometry optical waveguides

We calculate the effect of self-phase modulation of a pulse propagating in a long-geometry waveguide. Our calculations go beyond the usual theory, which does not take into account the envelope time variation in the nonlinear term of the wave equation. We show that for long waveguides with relatively small group-velocity dispersion but finite nonlinear coefficient $n_2$, the pulse will develop a sizable asymmetric frequency and temporal spectra.